
Recent progress in studies of cobalt-based quasi-1-dimensional quantum magnets
Lun Jin, Robert J. Cava
Front. Phys. ›› 2025, Vol. 20 ›› Issue (3) : 034301.
Recent progress in studies of cobalt-based quasi-1-dimensional quantum magnets
The interplay of crystal electric field, temperature, and spin–orbit coupling can yield a Kramer ion and thus an effective S = ½ ground state for ions (), which is often the case for low-dimensional materials. This is because a highly anisotropic structural motif can force the spins to point either “up” or “down,” thereby creating a system where spins communicate via Ising interactions. Cobalt-based quasi-1-dimensional materials have been studied in this context since the latter half of the 20th century. However, due to the development of modern characterization techniques and advances in sample preparation, the exotic physical phenomena that have generated the most interest have only emerged in the past three to four decades. This topical review mainly summarizes progress in cobalt-based quasi-1-dimensional quantum magnets and comments on a few research directions of potential future interest.
quasi-1-dimensional materials / quantum magnet / ${\color{khaki}{{\mathrm{Co}}^{2+}}} $ ion / Ising interaction / quantum phase transition / field-induced magnetic transition / magnetic frustration / quantum fluctuations
[1] |
S. Lee, R. K. Kaul, and L. Balents, Interplay of quantum criticality and geometric frustration in columbite, Nat. Phys. 6(9), 702 (2010)
CrossRef
ADS
arXiv
Google scholar
|
[2] |
T. Liang, S. M. Koohpayeh, J. W. Krizan, T. M. McQueen, R. J. Cava, and N. P. Ong, Heat capacity peak at the quantum critical point of the transverse Ising magnet CoNb2O6, Nat. Commun. 6(1), 7611 (2015)
CrossRef
ADS
arXiv
Google scholar
|
[3] |
G. H. Wannier, The triangular Ising net, Phys. Rev. 79, 357 (1950)
CrossRef
ADS
Google scholar
|
[4] |
W. Scharf, H. Weitzel, I. Yaeger, I. Maartense, and B. M. Wanklyn, Magnetic structures of CoNb2O6, J. Magn. Magn. Mater. 13(1−2), 121 (1979)
CrossRef
ADS
Google scholar
|
[5] |
V. Hardy, V. Caignaert, O. Pérez, L. Hervé, N. Sakly, B. Raveau, M. M. Seikh, and F. Damay, Pretransitional short-range ordering in a triangular lattice of Ising spin chains, Phys. Rev. B 98(14), 144414 (2018)
CrossRef
ADS
Google scholar
|
[6] |
H. Guo, L. Zhao, M. Baenitz, X. Fabrèges, A. Gukasov, A. Melendez Sans, D. I. Khomskii, L. H. Tjeng, and A. C. Komarek, Emergent 1/3 magnetization plateaus in pyroxene CoGeO3, Phys. Rev. Res. 3(3), L032037 (2021)
CrossRef
ADS
arXiv
Google scholar
|
[7] |
L. Jin,S. Peng,A. Nakano Rutherford,X. Xu,D. Ni, C. Yang,Y. Ji Byeon,W. Xie,H. Zhou,X. Dai, R. J. Cava, A pyroxene-based quantum magnet with multiple magnetization plateaus, Sci. Adv. 10(41), eadp4685 (2024)
|
[8] |
S. Agrestini, L. C. Chapon, A. Daoud-Aladine, J. Schefer, A. Gukasov, C. Mazzoli, M. R. Lees, and O. A. Petrenko, Nature of the magnetic order in Ca3Co2O6, Phys. Rev. Lett. 101(9), 097207 (2008)
CrossRef
ADS
arXiv
Google scholar
|
[9] |
S. Kobayashi, S. Mitsuda, and K. Prokes, Low-temperature magnetic phase transitions of the geometrically frustrated isosceles triangular Ising antiferromagnet CoNb2O6, Phys. Rev. B 63(2), 024415 (2000)
CrossRef
ADS
Google scholar
|
[10] |
E. Canévet, B. Grenier, M. Klanjšek, C. Berthier, M. Horvatić, V. Simonet, and P. Lejay, Field-induced magnetic behavior in quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8: A single-crystal neutron diffraction study, Phys. Rev. B 87(5), 054408 (2013)
CrossRef
ADS
arXiv
Google scholar
|
[11] |
A. B. Zamolodchikov, Integrals of motion and S-matrix of the (scaled) T = Tc Ising model with magnetic field, Int. J. Mod. Phys. A 4(16), 4235 (1989)
CrossRef
ADS
Google scholar
|
[12] |
S. Sachdev, Physics World Quantum phase transitions, Cambridge University Press, 1999
|
[13] |
S. Ghosh, T. F. Rosenbaum, G. Aeppli, and S. N. Coppersmith, Entangled quantum state of magnetic dipoles, Nature 425(6953), 48 (2003)
CrossRef
ADS
Google scholar
|
[14] |
R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Quantum criticality in an Ising chain: Experimental evidence for emergent E8 symmetry, Science 327(5962), 177 (2010)
CrossRef
ADS
arXiv
Google scholar
|
[15] |
E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. 16(3), 407 (1961)
CrossRef
ADS
Google scholar
|
[16] |
T. Hanawa, K. Shinkawa, M. Ishikawa, K. Miyatani, K. Saito, and K. Kohn, Anisotropic specific heat of CoNb2O6 in magnetic fields, J. Phys. Soc. Jpn. 63(7), 2706 (1994)
CrossRef
ADS
Google scholar
|
[17] |
C. Heid, H. Weitzel, P. Burlet, M. Bonnet, W. Gonschorek, T. Vogt, J. Norwig, and H. Fuess, Magnetic phase diagram of CoNb2O6: A neutron diffraction study, J. Magn. Magn. Mater. 151(1−2), 123 (1995)
CrossRef
ADS
Google scholar
|
[18] |
S. Kobayashi,S. Mitsuda,K. Hosoya,H. Yoshizawa,T. Hanawa,M. Ishikawa,K. Miyatani,K. Saito,K. Kohn, Competition between the inter-chain interaction and single-ion anisotropy in CoNb2O6, Physica B 213–214, 176 (1995)
|
[19] |
S. Kobayashi, S. Mitsuda, M. Ishikawa, K. Miyatani, and K. Kohn, Three-dimensional magnetic ordering in the quasi-one-dimensional Ising magnet CoNb2O6 with partially released geometrical frustration, Phys. Rev. B 60(5), 3331 (1999)
CrossRef
ADS
Google scholar
|
[20] |
A. W. Kinross, M. Fu, T. J. Munsie, H. A. Dabkowska, G. M. Luke, S. Sachdev, and T. Imai, Evolution of quantum fluctuations near the quantum critical point of the transverse field ising chain system CoNb2O6, Phys. Rev. X 4(3), 031008 (2014)
CrossRef
ADS
arXiv
Google scholar
|
[21] |
K. Matsuura, P. T. Cong, S. Zherlitsyn, J. Wosnitza, N. Abe, and T. H. Arima, Anomalous lattice softening near a quantum critical point in a transverse Ising magnet, Phys. Rev. Lett. 124(12), 127205 (2020)
CrossRef
ADS
Google scholar
|
[22] |
C. M. Morris, R. Valdés Aguilar, A. Ghosh, S. M. Koohpayeh, J. Krizan, R. J. Cava, O. Tchernyshyov, T. M. McQueen, and N. P. Armitage, Hierarchy of bound states in the one-dimensional ferromagnetic Ising chain CoNb2O6 investigated by high-resolution time-domain terahertz spectroscopy, Phys. Rev. Lett. 112(13), 137403 (2014)
CrossRef
ADS
arXiv
Google scholar
|
[23] |
J. A. Kjäll,F. Pollmann,J. E. Moore, Bound states and E8 symmetry effects in perturbed quantum Ising chains, Phys. Rev. B 83, 020407(R) (2011)
|
[24] |
N. J. Robinson, F. H. L. Essler, I. Cabrera, and R. Coldea, Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6, Phys. Rev. B 90(17), 174406 (2014)
CrossRef
ADS
arXiv
Google scholar
|
[25] |
M. Fava, R. Coldea, and S. A. Parameswaran, Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb2O6, Proc. Natl. Acad. Sci. USA 117(41), 25219 (2020)
CrossRef
ADS
arXiv
Google scholar
|
[26] |
C. L. Sarkis, S. Säubert, V. Williams, E. S. Choi, T. R. Reeder, H. S. Nair, and K. A. Ross, Low-temperature domain-wall freezing and nonequilibrium dynamics in the transverse-field Ising model material CoNb2O6, Phys. Rev. B 104(21), 214424 (2021)
CrossRef
ADS
arXiv
Google scholar
|
[27] |
L. Woodland, D. Macdougal, I. M. Cabrera, J. D. Thompson, D. Prabhakaran, R. I. Bewley, and R. Coldea, Tuning the confinement potential between spinons in the Ising chain compound CoNb2O6 using longitudinal fields and quantitative determination of the microscopic Hamiltonian, Phys. Rev. B 108(18), 184416 (2023)
CrossRef
ADS
arXiv
Google scholar
|
[28] |
S. Birnkammer, J. Knolle, and M. Knap, Signatures of domain-wall confinement in Raman spectroscopy of Ising spin chains, Phys. Rev. B 110(13), 134408 (2024)
CrossRef
ADS
arXiv
Google scholar
|
[29] |
C. M. Morris, N. Desai, J. Viirok, D. Hüvonen, U. Nagel, T. Rõõm, J. W. Krizan, R. J. Cava, T. M. McQueen, S. M. Koohpayeh, R. K. Kaul, and N. P. Armitage, Duality and domain wall dynamics in a twisted Kitaev chain, Nat. Phys. 17(7), 832 (2021)
CrossRef
ADS
arXiv
Google scholar
|
[30] |
D. Churchill and H. Y. Kee, Transforming from Kitaev to disguised Ising chain: Application to CoNb2O6, Phys. Rev. Lett. 133(5), 056703 (2024)
CrossRef
ADS
arXiv
Google scholar
|
[31] |
J. N. Reimers, J. E. Greedan, C. V. Stager, and R. Kremer, Crystal structure and magnetism in CoSb2O6 and CoTa2O6, J. Solid State Chem. 83(1), 20 (1989)
CrossRef
ADS
Google scholar
|
[32] |
I. S. Mulla,N. Natarajan,A. B. Gaikwad,V. Samuel,U. N. Guptha,V. Ravi, A coprecipitation technique to prepare CoTa2O6 and CoNb2O6, Mater. Lett. 61(11–12), 2127 (2007)
|
[33] |
E. J. Kinast, C. A. dos Santos, D. Schmitt, O. Isnard, M. A. Gusmão, and J. B. M. da Cunha, Magnetic structure of the quasi-two-dimensional compound CoTa2O6, J. Alloys Compd. 491(1−2), 41 (2010)
CrossRef
ADS
Google scholar
|
[34] |
A. B. Christian, A. T. Schye, K. O. White, and J. J. Neumeier, Magnetic, thermal, and optical properties of single-crystalline CoTa2O6 and FeTa2O6 and their anisotropic magnetocaloric effect, J. Phys.: Condens. Matter 30(19), 195803 (2018)
CrossRef
ADS
Google scholar
|
[35] |
Z. He and M. Itoh, Single crystal flux growth of the Ising spin-chain system γ-CoV2O6, J. Cryst. Growth 388, 103 (2014)
CrossRef
ADS
Google scholar
|
[36] |
S. A. J. Kimber, H. Mutka, T. Chatterji, T. Hofmann, P. F. Henry, H. N. Bordallo, D. N. Argyriou, and J. P. Attfield, Metamagnetism and soliton excitations in the modulated ferromagnetic Ising chain CoV2O6, Phys. Rev. B 84(10), 104425 (2011)
CrossRef
ADS
arXiv
Google scholar
|
[37] |
M. Markkula, A. M. Arévalo-López, and J. P. Attfield, Field-induced spin orders in monoclinic CoV2O6, Phys. Rev. B 86(13), 134401 (2012)
CrossRef
ADS
Google scholar
|
[38] |
M. Markkula, A. M. Arévalo-López, and J. P. Attfield, Neutron diffraction study of monoclinic brannerite-type CoV2O6, J. Solid State Chem. 192, 390 (2012)
CrossRef
ADS
Google scholar
|
[39] |
M. Lenertz, J. Alaria, D. Stoeffler, S. Colis, A. Dinia, O. Mentré, G. André, F. Porcher, and E. Suard, Magnetic structure of ground and field-induced ordered states of low-dimensional α-CoV2O6: Experiment and theory, Phys. Rev. B 86(21), 214428 (2012)
CrossRef
ADS
Google scholar
|
[40] |
A. Saúl, D. Vodenicarevic, and G. Radtke, Theoretical study of the magnetic order in α-CoV2O6, Phys. Rev. B 87(2), 024403 (2013)
CrossRef
ADS
Google scholar
|
[41] |
Z. He, J. I. Yamaura, Y. Ueda, and W. Cheng, CoV2O6 single crystals grown in a closed crucible: Unusual magnetic behaviors with large anisotropy and 1/3 magnetization plateau, J. Am. Chem. Soc. 131(22), 7554 (2009)
CrossRef
ADS
Google scholar
|
[42] |
Y. Drees, S. Agrestini, O. Zaharko, and A. C. Komarek, Floating zone single crystal growth of γ-CoV2O6 with substantially enhanced crystal size and quality, Cryst. Growth Des. 15(3), 1168 (2015)
CrossRef
ADS
Google scholar
|
[43] |
Y. Zhao, Z. Ma, Z. He, H. Liao, Y. C. Wang, J. Wang, and Y. Li, Quantum annealing of a frustrated magnet, Nat. Commun. 15(1), 3495 (2024)
CrossRef
ADS
arXiv
Google scholar
|
[44] |
G. Durand, S. Vilminot, P. Rabu, A. Derory, J. P. Lambour, E. Ressouche, Synthesis, structure, and magnetic properties of CaMSi2O6 (M= Co, Ni) compounds and their solid solutions, J. Solid State Chem. 124(2), 374 (1996)
CrossRef
ADS
Google scholar
|
[45] |
G. J. Redhammer, G. Roth, W. Treutmann, W. Paulus, G. André, C. Pietzonka, G. Amthauer, Magnetic ordering, spin structure in Ca-bearing clinopyroxenes CaM2+(Si, Ge)2O6, M=Fe, Ni, and Co, Mn, J. Solid State Chem. 181(11), 3163 (2008)
CrossRef
ADS
Google scholar
|
[46] |
S. Jodlauk, P. Becker, J. A. Mydosh, D. I. Khomskii, T. Lorenz, S. V. Streltsov, D. C. Hezel, and L. Bohatý, Pyroxenes: A new class of multiferroics, J. Phys.: Condens. Matter 19(43), 432201 (2007)
CrossRef
ADS
arXiv
Google scholar
|
[47] |
I. Kim, B. G. Jeon, D. Patil, S. Patil, G. Nénert, and K. H. Kim, Observation of multiferroic properties in pyroxene NaFeGe2O6, J. Phys.: Condens. Matter 24(30), 306001 (2012)
CrossRef
ADS
Google scholar
|
[48] |
M. Ackermann, L. Andersen, T. Lorenz, L. Bohatý, and P. Becker, Anisotropy study of multiferroicity in the pyroxene NaFeGe2O6, New J. Phys. 17(1), 013045 (2015)
CrossRef
ADS
arXiv
Google scholar
|
[49] |
L. Ding, C. V. Colin, C. Darie, J. Robert, F. Gay, and P. Bordet, One-dimensional short-range magnetic correlations in the magnetoelectric pyroxene CaMnGe2O6, Phys. Rev. B 93(6), 064423 (2016)
CrossRef
ADS
Google scholar
|
[50] |
G. J. Redhammer, G. Roth, A. Senyshyn, G. Tippelt, C. Pietzonka, Crystal , and magnetic spin structure of Germanium-Hedenbergite, CaFeGe2O6, and a comparison with other magnetic/magnetoelectric/ multiferroic pyroxenes, Z. Kristallogr. Cryst. Mater. 228(3), 140 (2013)
CrossRef
ADS
Google scholar
|
[51] |
J. O’Connell, X. Xu, L. Jin, and R. J. Cava, The ferromagnetic to antiferromagnetic crossover in chromium-based pyroxenes tuned via the Ge to Si ratio, J. Solid State Chem. 339, 124919 (2024)
CrossRef
ADS
Google scholar
|
[52] |
L. Zhao, Z. Hu, H. Guo, C. Geibel, H. J. Lin, C. T. Chen, D. Khomskii, L. H. Tjeng, and A. C. Komarek, Single crystal growth and physical properties of pyroxene CoGeO3, Crystals (Basel) 11(4), 378 (2021)
CrossRef
ADS
arXiv
Google scholar
|
[53] |
P. A. Maksimov, A. V. Ushakov, A. F. Gubkin, G. J. Redhammer, S. M. Winter, A. I. Kolesnikov, A. M. dos Santos, Z. Gai, M. A. McGuire, A. Podlesnyak, and S. V. Streltsov, Cobalt-based pyroxenes: A new playground for Kitaev physics, Proc. Natl. Acad. Sci. USA 121(43), e2409154121 (2024)
CrossRef
ADS
arXiv
Google scholar
|
[54] |
A. Okutani, T. Kida, T. Usui, T. Kimura, K. Okunishi, and M. Hagiwara, High field magnetization of single crystals of the S=1/2 quasi-1D Ising-like antiferromagnet SrCo2V2O8, Phys. Procedia 75, 779 (2015)
CrossRef
ADS
Google scholar
|
[55] |
Q. Faure, S. Takayoshi, S. Petit, V. Simonet, S. Raymond, L. P. Regnault, M. Boehm, J. S. White, M. Månsson, C. Rüegg, P. Lejay, B. Canals, T. Lorenz, S. C. Furuya, T. Giamarchi, and B. Grenier, Topological quantum phase transition in the Ising-like antiferromagnetic spin chain BaCo2V2O8, Nat. Phys. 14(7), 716 (2018)
CrossRef
ADS
arXiv
Google scholar
|
[56] |
S. Kimura, H. Yashiro, M. Hagiwara, K. Okunishi, K. Kindo, Z. He, T. Taniyama, and M. Itoh, High field magnetism of the quasi one-dimensional anisotropic antiferromagnet BaCo2V2O8, J. Phys.: Conf. Ser. 51, 99 (2006)
CrossRef
ADS
Google scholar
|
[57] |
B. Grenier, S. Petit, V. Simonet, E. Canévet, L. P. Regnault, S. Raymond, B. Canals, C. Berthier, and P. Lejay, Longitudinal and transverse Zeeman ladders in the Ising-like chain antiferromagnet BaCo2V2O8, Phys. Rev. Lett. 114(1), 017201 (2015)
CrossRef
ADS
arXiv
Google scholar
|
[58] |
Z. Wang,M. Schmidt,A. K. Bera,A. T. M. N. Islam,B. Lake,A. Loidl,J. Deisenhofer, Spinon confinement in the one-dimensional Ising-like antiferromagnet SrCo2V2O8, Phys. Rev. B 91, 140404(R) (2015)
|
[59] |
A. K. Bera, B. Lake, F. H. L. Essler, L. Vanderstraeten, C. Hubig, U. Schollwöck, A. T. M. N. Islam, A. Schneidewind, and D. L. Quintero-Castro, Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet, Phys. Rev. B 96(5), 054423 (2017)
CrossRef
ADS
arXiv
Google scholar
|
[60] |
S. Kimura, K. Okunishi, M. Hagiwara, K. Kindo, Z. He, T. Taniyama, M. Itoh, K. Koyama, and K. Watanabe, Collapse of magnetic order of the quasi one-dimensional ising-like antiferromagnet BaCo2V2O8 in transverse fields, J. Phys. Soc. Jpn. 82(3), 033706 (2013)
CrossRef
ADS
Google scholar
|
[61] |
S. K. Niesen, G. Kolland, M. Seher, O. Breunig, M. Valldor, M. Braden, B. Grenier, and T. Lorenz, Magnetic phase diagrams, domain switching, and quantum phase transition of the quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8, Phys. Rev. B 87(22), 224413 (2013)
CrossRef
ADS
arXiv
Google scholar
|
[62] |
Y. Cui, H. Zou, N. Xi, Z. He, Y. X. Yang, L. Shu, G. H. Zhang, Z. Hu, T. Chen, R. Yu, J. Wu, and W. Yu, Quantum criticality of the Ising-like screw chain antiferromagnet SrCo2V2O8 in a transverse magnetic field, Phys. Rev. Lett. 123(6), 067203 (2019)
CrossRef
ADS
arXiv
Google scholar
|
[63] |
Q. Faure, S. Takayoshi, B. Grenier, S. Petit, S. Raymond, M. Boehm, P. Lejay, T. Giamarchi, and V. Simonet, Solitonic excitations in the Ising anisotropic chain BaCo2V2O8 under large transverse magnetic field, Phys. Rev. Res. 3(4), 043227 (2021)
CrossRef
ADS
Google scholar
|
[64] |
Z. Zhang,K. Amelin,X. Wang,H. Zou,J. Yang, U. Nagel,T. Rõõm,T. Dey, A. A. Nugroho,T. Lorenz,J. Wu, Z. Wang, Observation of E8 particles in an Ising chain antiferromagnet, Phys. Rev. B 101, 220411(R) (2020)
|
[65] |
X. Wang, K. Puzniak, K. Schmalzl, C. Balz, M. Matsuda, A. Okutani, M. Hagiwara, J. Ma, J. Wu, and B. Lake, Spin dynamics of the E8 particles, Sci. Bull. (Beijing) 69(19), 2974 (2024)
CrossRef
ADS
arXiv
Google scholar
|
[66] |
H. Zou,Y. Cui,X. Wang,Z. Zhang,J. Yang, G. Xu,A. Okutani,M. Hagiwara,M. Matsuda,G. Wang, G. Mussardo,K. Hódsági,M. Kormos,Z. He, S. Kimura,R. Yu,W. Yu,J. Ma,J. Wu, E8 spectra of quasi-one-dimensional antiferromagnet BaCo2V2O8 under transverse field, Phys. Rev. Lett. 127(7), 077201 (2021)
|
[67] |
X. Wang, H. Zou, K. Hódsági, M. Kormos, G. Takács, and J. Wu, Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain, Phys. Rev. B 103(23), 235117 (2021)
CrossRef
ADS
arXiv
Google scholar
|
[68] |
B. Grenier, V. Simonet, B. Canals, P. Lejay, M. Klanjšek, M. Horvatić, and C. Berthier, Neutron diffraction investigation of the H-T phase diagram above the longitudinal incommensurate phase of BaCo2V2O8, Phys. Rev. B 92(13), 134416 (2015)
CrossRef
ADS
Google scholar
|
[69] |
L. Shen, O. Zaharko, J. O. Birk, E. Jellyman, Z. He, and E. Blackburn, Magnetic phase diagram of the quantum spin chain compound SrCo2V2O8: A single-crystal neutron diffraction study, New J. Phys. 21(7), 073014 (2019)
CrossRef
ADS
arXiv
Google scholar
|
[70] |
H. Von Bethe, Zur theorie der metalle, Eur. Phys. J. A 71(3−4), 205 (1931)
CrossRef
ADS
Google scholar
|
[71] |
Z. Wang, J. Wu, W. Yang, A. K. Bera, D. Kamenskyi, A. T. M. N. Islam, S. Xu, J. M. Law, B. Lake, C. Wu, and A. Loidl, Experimental observation of Bethe strings, Nature 554(7691), 219 (2018)
CrossRef
ADS
arXiv
Google scholar
|
[72] |
Z. Wang, M. Schmidt, A. Loidl, J. Wu, H. Zou, W. Yang, C. Dong, Y. Kohama, K. Kindo, D. I. Gorbunov, S. Niesen, O. Breunig, J. Engelmayer, and T. Lorenz, Quantum critical dynamics of a Heisenberg−Ising chain in a longitudinal field: Many-body strings versus fractional excitations, Phys. Rev. Lett. 123(6), 067202 (2019)
CrossRef
ADS
arXiv
Google scholar
|
[73] |
A. K. Bera, J. Wu, W. Yang, R. Bewley, M. Boehm, J. Xu, M. Bartkowiak, O. Prokhnenko, B. Klemke, A. T. M. N. Islam, J. M. Law, Z. Wang, and B. Lake, Dispersions of many-body Bethe strings, Nat. Phys. 16(6), 625 (2020)
CrossRef
ADS
arXiv
Google scholar
|
[74] |
Z. He, Y. Ueda, and M. Itoh, Synthesis, structure and magnetic properties of new vanadate PbCo2V2O8, J. Solid State Chem. 180(5), 1770 (2007)
CrossRef
ADS
Google scholar
|
[75] |
Z. He, Y. Ueda, and M. Itoh, Field-induced order−disorder transition in quasi-one-dimensional spin system PbCo2V2O8, Solid State Commun. 142(7), 404 (2007)
CrossRef
ADS
Google scholar
|
[76] |
K. Puzniak, C. Aguilar-Maldonado, R. Feyerherm, K. Prokeš, A. T. M. N. Islam, Y. Skourski, L. Keller, and B. Lake, Magnetic structure and phase diagram of the Heisenberg–Ising spin chain antiferromagnetic PbCo2V2O8, Phys. Rev. B 108(14), 144432 (2023)
CrossRef
ADS
Google scholar
|
[77] |
H. Fjellvåg, E. Gulbrandsen, S. Aasland, A. Olsen, and B. C. Hauback, Crystal structure and possible charge ordering in one-dimensional Ca3Co2O6, J. Solid State Chem. 124(1), 190 (1996)
CrossRef
ADS
Google scholar
|
[78] |
C. Mazzoli, A. Bombardi, S. Agrestini, and M. R. Lees, Resonant X-ray scattering study of Ca3Co2O6 ground state: Preliminary results of magnetic field effects, Physica B 404(19), 3042 (2009)
CrossRef
ADS
Google scholar
|
[79] |
S. Aasland, H. Fjellvåg, and B. Haubackb, Magnetic properties of the one-dimensional Ca3Co2O6, Solid State Commun. 101(3), 187 (1997)
CrossRef
ADS
Google scholar
|
[80] |
H. Kageyama, K. Yoshimura, K. Kosuge, M. Azuma, M. Takano, H. Mitamura, and T. Goto, Magnetic anisotropy of Ca3Co2O6 with ferromagnetic Ising Chains, J. Phys. Soc. Jpn. 66(12), 3996 (1997)
CrossRef
ADS
Google scholar
|
[81] |
A. Maignan, C. Michel, A. C. Masset, C. Martin, and B. Raveau, Single crystal study of the one dimensional Ca3Co2O6 compound: Five stable configurations for the Ising triangular lattice, Eur. Phys. J. B 15(4), 657 (2000)
CrossRef
ADS
Google scholar
|
[82] |
A. Maignan, V. Hardy, S. Hébert, M. Drillon, M. R. Lees, O. Petrenko, D. M. K. Paul, and D. Khomskii, Quantum tunneling of the magnetization in the Ising chain compound Ca3Co2O6, J. Mater. Chem. 14(8), 1231 (2004)
CrossRef
ADS
Google scholar
|
[83] |
R. Vidya, P. Ravindran, H. Fjellvåg, A. Kjekshus, and O. Eriksson, Tailor-made electronic and magnetic properties in one-dimensional pure and Y-substituted Ca3Co2O6, Phys. Rev. Lett. 91(18), 186404 (2003)
CrossRef
ADS
Google scholar
|
[84] |
V. Hardy, S. Lambert, R. Lees, and D. McK. Paul, Specific heat and magnetization study on single crystals of the frustrated quasi-one-dimensional oxide Ca3Co2O6, Phys. Rev. B 68, 014424 (2003)
CrossRef
ADS
Google scholar
|
[85] |
V. Eyert, C. Laschinger, T. Kopp, and R. Frésard, Extended moment formation and magnetic ordering in the trigonal chain compound Ca3Co2O6, Chem. Phys. Lett. 385(3−4), 249 (2004)
CrossRef
ADS
Google scholar
|
[86] |
H. Wu, M. W. Haverkort, Z. Hu, D. I. Khomskii, and L. H. Tjeng, Nature of magnetism in Ca3Co2O6, Phys. Rev. Lett. 95(18), 186401 (2005)
CrossRef
ADS
Google scholar
|
[87] |
K. Takubo, T. Mizokawa, S. Hirata, J. Y. Son, A. Fujimori, D. Topwal, D. D. Sarma, S. Rayaprol, and E. V. Sampathkumaran, Electronic structure of Ca3CoXO6 (X=Co, Rh, Ir) studied by X-ray photoemission spectroscopy, Phys. Rev. B 71(7), 073406 (2005)
CrossRef
ADS
Google scholar
|
[88] |
T. Burnus, Z. Hu, M. W. Haverkort, J. C. Cezar, D. Flahaut, V. Hardy, A. Maignan, N. B. Brookes, A. Tanaka, H. H. Hsieh, H. J. Lin, C. T. Chen, and L. H. Tjeng, Valence, spin, and orbital state of Co ions in one-dimensional Ca3Co2O6: An X-ray absorption and magnetic circular dichroism study, Phys. Rev. B 74(24), 245111 (2006)
CrossRef
ADS
Google scholar
|
[89] |
L. C. Chapon, Origin of the long-wavelength magnetic modulation in Ca3Co2O6, Phys. Rev. B 80(17), 172405 (2009)
CrossRef
ADS
arXiv
Google scholar
|
[90] |
T. Moyoshi and K. Motoya, Incommensurate magnetic structure and its long-time variation in a geometrically frustrated magnet Ca3Co2O6, J. Phys. Soc. Jpn. 80(3), 034701 (2011)
CrossRef
ADS
Google scholar
|
[91] |
S. Agrestini,C. Mazzoli,A. Bombardi,M. R. Lees, Incommensurate magnetic ground state revealed by resonant X-ray scattering in the frustrated spin system Ca3Co2O6, Phys. Rev. B 77, 140403(R) (2008)
|
[92] |
P. Lampen, N. S. Bingham, M. H. Phan, H. Srikanth, H. T. Yi, and S. W. Cheong, Macroscopic phase diagram and magnetocaloric study of metamagnetic transitions in the spin chain system Ca3Co2O6, Phys. Rev. B 89(14), 144414 (2014)
CrossRef
ADS
Google scholar
|
[93] |
H. Kageyama, K. Yoshimura, K. Kosuge, H. Mitamura, and T. Goto, Field-induced magnetic transitions in the one-dimensional compound Ca3Co2O6, J. Phys. Soc. Jpn. 66(6), 1607 (1997)
CrossRef
ADS
Google scholar
|
[94] |
V. Hardy, M. R. Lees, O. A. Petrenko, D. M. K. Paul, D. Flahaut, S. Hébert, and A. Maignan, Temperature and time dependence of the field-driven magnetization steps in Ca3Co2O6 single crystals, Phys. Rev. B 70(6), 064424 (2004)
CrossRef
ADS
Google scholar
|
[95] |
Y. B. Kudasov, Steplike magnetization in a spin-chain system: Ca3Co2O6, Phys. Rev. Lett. 96(2), 027212 (2006)
CrossRef
ADS
Google scholar
|
[96] |
C. L. Fleck, M. R. Lees, S. Agrestini, G. J. McIntyre, and O. A. Petrenko, Field-driven magnetisation steps in Ca3Co2O6: A single-crystal neutron-diffraction study, Europhys. Lett. 90(6), 67006 (2010)
CrossRef
ADS
arXiv
Google scholar
|
[97] |
X. Y. Yao, S. Dong, and J. M. Liu, Steplike magnetization of spin chains in a triangular lattice: Monte Carlo simulations, Phys. Rev. B 73(21), 212415 (2006)
CrossRef
ADS
Google scholar
|
[98] |
X. Yao, S. Dong, H. Yu, and J. Liu, Monte Carlo simulation of magnetic behavior of a spin-chain system on a triangular lattice, Phys. Rev. B 74(13), 134421 (2006)
CrossRef
ADS
Google scholar
|
[99] |
M. H. Qin, K. F. Wang, and J. M. Liu, Two-step magnetization in a spin-chain system on the triangular lattice: Wang–Landau simulation, Phys. Rev. B 79(17), 172405 (2009)
CrossRef
ADS
Google scholar
|
[100] |
R. Soto, G. Martínez, M. N. Baibich, J. M. Florez, and P. Vargas, Metastable states in the triangular-lattice Ising model studied by Monte Carlo simulations: Application to the spin-chain compound Ca3Co2O6, Phys. Rev. B 79(18), 184422 (2009)
CrossRef
ADS
arXiv
Google scholar
|
[101] |
Y. B. Kudasov, A. S. Korshunov, V. N. Pavlov, and D. A. Maslov, Dynamics of magnetization in frustrated spin-chain system Ca3Co2O6, Phys. Rev. B 78(13), 132407 (2008)
CrossRef
ADS
arXiv
Google scholar
|
[102] |
J. A. M. Paddison, S. Agrestini, M. R. Lees, C. L. Fleck, P. P. Deen, A. L. Goodwin, J. R. Stewart, and O. A. Petrenko, Spin correlations in Ca3Co2O6: Polarized-neutron diffraction and Monte Carlo study, Phys. Rev. B 90(1), 014411 (2014)
CrossRef
ADS
arXiv
Google scholar
|
[103] |
I. Nekrashevich, X. Ding, F. Balakirev, H. T. Yi, S. W. Cheong, L. Civale, Y. Kamiya, and V. S. Zapf, Reaching the equilibrium state of the frustrated triangular Ising magnet Ca3Co2O6, Phys. Rev. B 105(2), 024426 (2022)
CrossRef
ADS
arXiv
Google scholar
|
[104] |
Y. Kamiya and C. D. Batista, Formation of magnetic microphases in Ca3Co2O6, Phys. Rev. Lett. 109(6), 067204 (2012)
CrossRef
ADS
arXiv
Google scholar
|
[105] |
Y. Kamiya, Magnetic field induced deformation of the spin density wave microphases in Ca3Co2O6, Phys. Rev. B 107(13), 134409 (2023)
CrossRef
ADS
arXiv
Google scholar
|
[106] |
S. Agrestini, C. L. Fleck, L. C. Chapon, C. Mazzoli, A. Bombardi, M. R. Lees, and O. A. Petrenko, Slow magnetic order–order transition in the spin chain antiferromagnet Ca3Co2O6, Phys. Rev. Lett. 106(19), 197204 (2011)
CrossRef
ADS
arXiv
Google scholar
|
[107] |
K. Motoya, T. Kihara, H. Nojiri, Y. Uwatoko, M. Matsuda, and T. Hong, Time and magnetic field variations of magnetic structure in the triangular lattice magnet Ca3Co2O6, J. Phys. Soc. Jpn. 87(11), 114703 (2018)
CrossRef
ADS
Google scholar
|
[108] |
D. P. Kozlenko, N. T. Dang, N. O. Golosova, S. E. Kichanov, E. V. Lukin, P. J. Lampen Kelley, E. M. Clements, K. V. Glazyrin, S. H. Jabarov, T. L. Phan, B. N. Savenko, H. Srikanth, and M. H. Phan, Pressure-induced modifications of the magnetic order in the spin-chain compound Ca3Co2O6, Phys. Rev. B 98(13), 134435 (2018)
CrossRef
ADS
Google scholar
|
[109] |
B. Leedahl, M. Sundermann, A. Amorese, A. Severing, H. Gretarsson, L. Zhang, A. C. Komarek, A. Maignan, M. W. Haverkort, and L. H. Tjeng, Origin of Ising magnetism in Ca3Co2O6 unveiled by orbital imaging, Nat. Commun. 10(1), 5447 (2019)
CrossRef
ADS
arXiv
Google scholar
|
[110] |
G. Allodi, P. Santini, S. Carretta, S. Agrestini, C. Mazzoli, A. Bombardi, M. R. Lees, and R. De Renzi, Exchange interactions in Ca3Co2O6 probed locally by NMR, Phys. Rev. B 89(10), 104401 (2014)
CrossRef
ADS
Google scholar
|
[111] |
J. Sugiyama, H. Nozaki, Y. Ikedo, K. Mukai, D. Andreica, A. Amato, J. H. Brewer, E. J. Ansaldo, G. D. Morris, T. Takami, and H. Ikuta, Evidence of two dimensionality in quasi-one-dimensional cobalt oxides, Phys. Rev. Lett. 96(19), 197206 (2006)
CrossRef
ADS
Google scholar
|
[112] |
Y. J. Choi, H. T. Yi, S. Lee, Q. Huang, V. Kiryukhin, and S. W. Cheong, Ferroelectricity in an Ising chain magnet, Phys. Rev. Lett. 100(4), 047601 (2008)
CrossRef
ADS
Google scholar
|
[113] |
H. Wu, T. Burnus, Z. Hu, C. Martin, A. Maignan, J. C. Cezar, A. Tanaka, N. B. Brookes, D. I. Khomskii, and L. H. Tjeng, Ising magnetism and ferroelectricity in Ca3CoMnO6, Phys. Rev. Lett. 102(2), 026404 (2009)
CrossRef
ADS
arXiv
Google scholar
|
[114] |
J. W. Kim, E. D. Mun, X. Ding, A. Hansen, M. Jaime, N. Harrison, H. T. Yi, Y. Chai, Y. Sun, S. W. Cheong, and V. S. Zapf, Metastable states in the frustrated triangular compounds Ca3Co2−xMnxO6 and Ca3Co2O6, Phys. Rev. B 98(2), 024407 (2018)
CrossRef
ADS
Google scholar
|
[115] |
S. Niitaka, K. Yoshimura, K. Kosuge, M. Nishi, and K. Kakurai, Partially disordered antiferromagnetic phase in Ca3CoRhO6, Phys. Rev. Lett. 87(17), 177202 (2001)
CrossRef
ADS
Google scholar
|
[116] |
M. H. Whangbo, D. Dai, H. J. Koo, and S. Jobic, Investigations of the oxidation states and spin distributions in Ca3Co2O6 and Ca3CoRhO6 by spin-polarized electronic band structure calculations, Solid State Commun. 125(7−8), 413 (2003)
CrossRef
ADS
Google scholar
|
[117] |
J. An and C. W. Nan, Electronic structure and transport of Ca3Co2O6 and Ca3CoNiO6, Solid State Commun. 129(1), 51 (2004)
CrossRef
ADS
Google scholar
|
[118] |
T. Takami,H. Ikuta,U. Mizutani, Thermoelectric properties of An+2Con+1O3n+3 (A = Ca, Sr, Ba, n = 1–5), Jpn. J. Appl. Phys. 43(12), 8208 (2004)
|
[119] |
J. Sugiyama, H. Nozaki, J. H. Brewer, E. J. Ansaldo, T. Takami, H. Ikuta, and U. Mizutani, Appearance of a two-dimensional antiferromagnetic order in quasi-one-dimensional cobalt oxides, Phys. Rev. B 72(6), 064418 (2005)
CrossRef
ADS
Google scholar
|
[120] |
J. Sugiyama, H. Nozaki, Y. Ikedo, K. Mukai, D. Andreica, A. Amato, J. H. Brewer, E. J. Ansaldo, G. D. Morris, T. Takami, and H. Ikuta, Two dimensionality in quasi-one-dimensional cobalt oxides confirmed by muon-spin spectroscopy, J. Magn. Magn. Mater. 310(2), 2719 (2007)
CrossRef
ADS
Google scholar
|
[121] |
M. A. Melkozerova and G. V. Bazuev, Quasi-one-dimensional oxides Sr4Co3−xMnxO9 (0 ≤ x ≤ 3): Synthesis and magnetic properties, Russ. J. Inorg. Chem. 51(3), 362 (2006)
CrossRef
ADS
Google scholar
|
[122] |
K. Boulahya, M. Parras, J. M. González-Calbet, and J. L. Martínez, Synthesis, structural characterization, and magnetic study of Sr4Mn2CoO9, Chem. Mater. 15(18), 3537 (2003)
CrossRef
ADS
Google scholar
|
[123] |
K. Boulahya, M. Hernando, M. Parras, and J. M. González-Calbet, New stabilized phases in the Sr/Ca–Mn–Co–O system: Structural-magnetic properties relationship, J. Mater. Chem. 17(16), 1620 (2007)
CrossRef
ADS
Google scholar
|
[124] |
M. M. Seikh, V. Caignaert, O. Perez, B. Raveau, and V. Hardy, Single-ion and single-chain magnetism in triangular spin-chain oxides, Phys. Rev. B 95(17), 174417 (2017)
CrossRef
ADS
Google scholar
|
[125] |
M. Hernando, K. Boulahya, M. Parras, A. Varela, J. M. González-Calbet, and J. L. Martínez, Structural and magnetic study of Sr3.3Ca0.7CoRh2O9: A new partially ordered antiferromagnetic system, Chem. Mater. 14(12), 4948 (2002)
CrossRef
ADS
Google scholar
|
[126] |
T. I. Chupakhina, M. A. Melkozerova, and G. V. Bazuev, Phase formation features and magnetic properties of complex oxides in the systems Sr–Co–M–O (M = Zn, Cu), Russ. J. Inorg. Chem. 58(3), 253 (2013)
CrossRef
ADS
Google scholar
|
[127] |
A. J. Neer, J. Milam-Guerrero, J. E. So, B. C. Melot, K. A. Ross, Z. Hulvey, C. M. Brown, A. A. Sokol, and D. O. Scanlon, Ising-like antiferromagnetism on the octahedral sublattice of a cobalt-containing garnet and the potential for quantum criticality, Phys. Rev. B 95(14), 144419 (2017)
CrossRef
ADS
Google scholar
|
[128] |
A. J. Neer, J. A. Milam-Guerrero, V. A. Fischer, M. Zheng, N. R. Spence, C. Cozzan, M. Gu, J. M. Rondinelli, C. M. Brown, and B. C. Melot, Magnetic-field-induced dielectric anomalies in cobalt-containing garnets, Inorg. Chem. 61(14), 5452 (2022)
CrossRef
ADS
Google scholar
|
[129] |
I. W. Johnstone, D. J. Lockwood, and M. W. C. Dharma-wardana, Influence of interchain coupling on the one-dimensional magnon Raman spectrum of CsCoBr3, Solid State Commun. 36(7), 593 (1980)
CrossRef
ADS
Google scholar
|
[130] |
W. P. Lehmann, W. Breitlingc, and R. Weber, Raman scattering study of spin dynamics in the quasi-1D Ising antiferromagnets CsCoCl3, and CsCoBr3, J. Phys. C 14(31), 4655 (1981)
CrossRef
ADS
Google scholar
|
[131] |
D. J. Lockwood and I. W. Johnstone, Raman scattering from magnons and excitons in the 3-D ordered phases of CsCoBr3, J. Appl. Phys. 53(11), 8169 (1982)
CrossRef
ADS
Google scholar
|
[132] |
F. Matsubara, S. Inawashiro, and H. Ohhara, On the magnetic Raman scattering in CsCoCl3, CsCoBr3 and RbCoCl3, J. Phys.: Condens. Matter 3(12), 1815 (1991)
CrossRef
ADS
Google scholar
|
[133] |
S. E. Nagler, W. J. L. Buyers, R. L. Armstrong, and B. Briat, Ising-like spin-, quasi-one-dimensional antiferromagnets: Spin-wave response in CsCoX3 salts, Phys. Rev. B 27(3), 1784 (1983)
CrossRef
ADS
Google scholar
|
[134] |
S. E. Nagler, W. J. L. Buyers, R. L. Armstrong, and B. Briat, Propagating domain walls in CsCoBr3, Phys. Rev. Lett. 49(8), 590 (1982)
CrossRef
ADS
Google scholar
|
[135] |
H. Yoshizawa, K. Hirakawa, S. K. Satija, and G. Shirane, Dynamical correlation functions in a one-dimensional Ising-like antiferromagnetic CsCoCl3: A neutron scattering study, Phys. Rev. B 23(5), 2298 (1981)
CrossRef
ADS
Google scholar
|
[136] |
J. Villain, Propagative spin relaxation in the Ising-like antiferromagnetic linear chain, Physica B+C 79(1), 1 (1975)
CrossRef
ADS
Google scholar
|
[137] |
S. E. Nagler, W. J. L. Buyers, R. L. Armstrong, and B. Briat, Solitons in the one-dimensional antiferromagnet CsCoBr3, Phys. Rev. B 28(7), 3873 (1983)
CrossRef
ADS
Google scholar
|
[138] |
H. Shiba, Quantization of magnetic excitation continuum due to lnterchain coupling in nearly one-dimensional Ising-like antiferromagnets, Prog. Theor. Phys. 64(2), 466 (1980)
CrossRef
ADS
Google scholar
|
[139] |
N. Ishimura and H. Shiba, Dynamical correlation functions of one-dimensional anisotropic Heisenberg model with spin 1/2. I. Ising-like antiferromagnets, Prog. Theor. Phys. 63(3), 743 (1980)
CrossRef
ADS
Google scholar
|
[140] |
F. Matsubara and S. Inawashiro, Pair states and bound states of solitons in an Ising-like S=1/2 antiferromagnet with a weak next-nearest-neighbor interaction on a linear chain, J. Phys. Soc. Jpn. 58(12), 4284 (1989)
CrossRef
ADS
Google scholar
|
[141] |
J. P. Goff, D. A. Tennant, and S. E. Nagler, Exchange mixing and soliton dynamics in the quantum spin chain CsCoCl3, Phys. Rev. B 52(22), 15992 (1995)
CrossRef
ADS
Google scholar
|
[142] |
R. Jorke and U. Durr, Properties of magnetic excitations in RbCoCl3, J. Phys. C 16(31), L1129 (1983)
CrossRef
ADS
Google scholar
|
[143] |
D. J. Lockwood, I. W. Johnstone, H. J. Labbet, and B. Briat, Raman scattering from the 1D antiferromagnets RbCoCl3 and RbNiCl3, J. Phys. C 16(33), 6451 (1983)
CrossRef
ADS
Google scholar
|
[144] |
M. Mena, N. Hänni, S. Ward, E. Hirtenlechner, R. Bewley, C. Hubig, U. Schollwöck, B. Normand, K. W. Krämer, D. F. McMorrow, and C. Rüegg, Thermal control of spin excitations in the coupled ising-chain material RbCoCl3, Phys. Rev. Lett. 124(25), 257201 (2020)
CrossRef
ADS
arXiv
Google scholar
|
[145] |
N. P. Hänni, D. Sheptyakov, M. Mena, E. Hirtenlechner, L. Keller, U. Stuhr, L. P. Regnault, M. Medarde, A. Cervellino, C. Rüegg, B. Normand, and K. W. Krämer, Magnetic order in the quasi-one-dimensional Ising system RbCoCl3, Phys. Rev. B 103(9), 094424 (2021)
CrossRef
ADS
arXiv
Google scholar
|
[146] |
M. G. Cottam and D. J. Lockwood, Zeeman-ladder analysis of the Raman magnon energies in the quasi-one-dimensional antiferromagnet RbCoCl3, Phys. Rev. B 105(6), 064411 (2022)
CrossRef
ADS
Google scholar
|
[147] |
M. G. Cottam and D. J. Lockwood, Unusual behaviour of the spin-phonon coupling in the quasi-one-dimensional antiferromagnet RbCoCl3, Sci. Rep. 12(1), 14065 (2022)
CrossRef
ADS
Google scholar
|
[148] |
S. Calder, L. D. Sanjeewa, V. O. Garlea, J. Xing, R. J. Terry, and J. W. Kolis, Magnetic interactions in the one-dimensional spin-chain metal–organic compounds M(N2H5)2(SO4)2 (M=Cu, Co, Mn), Phys. Rev. Mater. 6(12), 124407 (2022)
CrossRef
ADS
Google scholar
|
[149] |
M. Böhme, M. Rams, C. Krebs, S. Mangelsen, I. Jess, W. Plass, and C. Näther, Co(NCS)2 chain compound with alternating 5- and 6-fold coordination: Influence of metal coordination on the magnetic properties, Inorg. Chem. 61(42), 16841 (2022)
CrossRef
ADS
Google scholar
|
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〈 |
|
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